Write the equation for each line. Use slope-intercept form. m = - 3/8 and the y -intercept is (0,12) .

The value of f(x)= (x-3).g(x)+8

A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of Euclidean division.

dividend= divisor x quotient+ remainder

given that, f(x) has remainder 8 and divided by x-3

as per division algorithm we can say that

dividend= divisor x quotient+ remainder

f(x)= (x-3).g(x)+ 8

if we need to find f(3) then put 3 in the place of x

that gives you f(3) = (3-3).g(x)+ 8

                        f(3)= 8

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The answer to f(x)= (x-3). g(x)+8

An algorithm for dividing two integers, N and D, into their quotient and/or remainder, or the product of Euclidean division, is known as a division algorithm.

Dividend equals Divisor x Quotient plus Remainder.

Given that, f(x) is divided by x-3 and has a remainder of 8.

The division algorithm allows us to state that

Dividend equals Divisor x Quotient plus Remainder.

f(x)= (x-3) (x-3).

g(x)+ 8

If we need to find f(3), we should substitute 3 for x.

giving you f(3) = (3-3).

g(x)+ 8

f(3)= 8

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The equation of the line in slope-intercept form is  y = (2/5)x + (-3/2)  .

The equation of a line in slope-intercept form can be written as follows,

y = mx + c                                                       equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is (x/6) - (5/12)y = 5/8 .

To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as

(x/6) - (5/12)y = 5/8

On multiplying both sides of above equation by (12/5), we will get

   (2/5)x - y = 3/2

⇒ y = (2/5)x + (-3/2)                                                 equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = 2/5

Intercept = c = -3/2

The equation of the line in slope-intercept form is  y = (2/5)x + (-3/2) .      

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The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

By the Exterior Angle Inequality Theorem, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .

Therefore, the correct answer is ∠ 7 and ∠ 8.

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Answer:

-1/2

[tex] - \frac{1 }{2} [/tex]

First the two fours cancel out so it's becomes

[tex] \frac{1 - 3}{4} [/tex]

then subtract

[tex] \frac{ - 2}{4} [/tex]

simplify

[tex] \frac{ - 1}{2} [/tex]

The number of days Bilquis can afford to rent while staying within her budget is 2 days.

The question has the following data

amount charged =  $48

Rent per mile = $0.08

The mile to drive = 175 miles.

Amount to spend = 110 dollars

The inequality would be written as

48x + 0.08(175) ≤ 110

we are to solve for the value of x

this would be

48x + 14 ≤ 110

48x ≤ 110 - 14

48x ≤ 96

We have to divide through by 48

x ≤ 96 / 48

x ≤ 2

Hence we can say that the number of days Bilquis can afford to rent while staying within her budget is 2 days.

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The following set of numbers, 15, 36, and 39, can be the measures of the sides of a right triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 15, b = 36, and c = 39

a + b > c     15 + 36 > 39     51 > 39     True

a + c > b     15 + 39 > 36     54 > 36     True

b + c > a     36 + 39 > 15     75 > 15     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

15^2 + 36^2 = 1521

2. Compare it to the square of the largest side.

39^2 = 1521

1521 = 1521

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 15, 36, and 39 can be the measure of the sides of a right triangle.

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Answer:

13.9

Step-by-step explanation:

13.891

the 9 is greater than 4 so it can round up the 8 to a 9

   The function y = 6x - x² + 1 already defined is a quadratic function.

 A function is the definition of a mathematical expression or equation that helps us to give a visual representation, through graphs to analyze the behavior of the same, a function is not real when it cuts the vertical axis at a same point of x.

      The given function is given by means of the expression

y=6x -x²+1

y = -x² + 6x + 1 , it is a quadratic function because of its exponent "2".

 Where we can separate each of the terms or parts:

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Answer:

32

Step-by-step explanation:

Step-by-step explanation:

If he doubles the amount of money he has now, he will have enough to buy the game with $8 left over. 2x=56+8 ; 2x=64 ; x=64/2 ; x=32. Skylar has $32 right now.Nov 12, 2020©

On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .

The quantity 3.185 times ten raised to the seventeenth power can written as 3.185 × [tex]10^{17}[/tex] .

The quantity 9.1 times ten raised to the eighth power can written as 9.1 × [tex]10^{8}[/tex] .

On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] ,

( 3.185 × [tex]10^{17}[/tex] )/( 9.1 × [tex]10^{8}[/tex] ) = 0.35 × [tex]10^{17-8}[/tex] = 0.35 ×[tex]10^{9}[/tex] = 3.5 ×[tex]10^{8}[/tex] (in scientific notation)

Scientific notation is a floating-point system in which the numbers are expressed as the products consisting of a number between one to ten multiplied by an appropriate power of ten.

On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .

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Answer:

Step-by-step explanation:

A sloping line on a speed-time graph represents an acceleration . The sloping line shows that the speed of the object is changing. The object is either speeding up or slowing down. The steeper the slope of the line the greater the acceleration.

The value of x is 15.

(3 - x/2) - (1 - x/3) = 7 - (x - x/2)

(6 - x/2) - (3 - x/3)  = 7 - (2x - x/2)

(6 - x/2) - (3 - x/3) =14 - 2x +x /2

by solving these equations we get ,

18 - x -6 = 42 - 3x

12 - 42 = - 2x

where, x = 15 .

therefore the value of x is 15.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

examples of equation and expression.

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Answer:

5(2.47y−2.03)

Use the distributive property to multiply 5 by 2.47y−2.03.

12.35y−10.15

Step-by-step explanation:

They can set up total 30 tables in 5 hours.

Multiply in mathematics refers to the continual addition of sets of same size.

2 × 3 = 6

It can be interpreted this way:

Three times two equals six.

Three times two equals six.

Six is two threes.

Given,

Andersons can set up 6 tables in 1 hour

Tables they can set up in 5 hours = 5 × 6

= 30

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Answer:

Step-by-step explanation:

Angle (3x+31)° and angle (2x-6)° are supplementary angles

(3x + 31)° + (2x - 6)° = 180°

5x + 25° = 180°

5x = 155°

x = 31°

-----------------

check

3 * 31 + 31 + 2 * 31 - 6 = 180

180 = 180           (remember PEMDAS)

the answer is good

Answer:

x=2

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

3(4x-2)=2(5x+3)

12x-6=10x+6

    +6       +6

12x=10x+12

-10x -10x

2x=12

Divide by 2.

x=6

Hope this helps.

The equation of the circle with radius 1 and center at (-6 , 10) is (x + 6)^2 + (y - 10)^2 = 1.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (-6 , 10)

r = 1

(x - -6)^2 + (y - 10)^2 = 1^2

(x + 6)^2 + (y - 10)^2 = 1

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AA=60+1.50x and BB=30+2.50x are the two required situations and  the number miles driven, x,x, that would make the cost of each company the same is 30.

Two expressions with equal sign is called as Equation.

Company A charges an initial fee of $60 for the rental plus $1.50 per mile driven= 60+1.50x

Company B charges an initial fee of $30 for the rental plus $2.50 per mile driven=30+2.50x.

60+1.50x=30+2.50x

60-30=2.50x-1.50x

30=x

Therefore, AA=60+1.50x and BB=30+2.50x are the two required situations and  the number miles driven, x,x, that would make the cost of each company the same is 30.

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9.233050612 is a rational number.

Real numbers that can be expressed as a ratio of two integers, such as P/Q, where Q is not equal to zero, are referred to as rational numbers. Finite or repeating numbers are included in the category of rational numbers.

Real numbers are referred to as irrational numbers if they cannot be represented as the ratio of two integers. These are composed entirely of non-terminating, non-repeating numbers.

The given number 9.233050612 can be written in the form P/Q as :

9.233050612 = [tex]\frac{9.233050612}{1000000000}[/tex]

Hence, the given number is a rational number.

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The correct question is:

"9.233050612 is a rational or irrational number"

Answer:

x+6/4=13

Step-by-step explanation:

the result is 11.5

Answer:

A=h(b+c) solve for c

First, multiply h to b and c

A = hb + hc

Then, transfer hb to the other side and change its sign from positive to negative.

A – hb = hc

To get c, Divide both sides by h

(A – hb)/h = hc/h

(A - hb)/h = c  OR c = (A – hb)/h

Example. Let us assume the following. A = 500 ; h= 10;b= 20; c= ?

c = (A – hb)/h

c = (500 – (10*20))/10

c = (500 – 200)/10

c =  300/10

c = 30

To check; use the original equation given.

A = h(b+c)

A = 10(20+30)

A = 200 + 300

A = 500. same as the figure given in the example.

[tex]\displaystyle\\Answer:\ b=\frac{A-hc}{h}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\A=h(b+c)\\A=hb+hc\\A-hc=hb+hc-hc\\A-hc=hb\\Divide\ both\ parts\ of\ the\ equation\ by\ h(h\neq 0):\\\frac{A-hc}{h}=b\\ Hence,\\b=\frac{A-hc}{h}[/tex]

Answer:

[tex]\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]

Step-by-step explanation:

In triangle ABD,

[tex]\sin 72^{\circ}=\frac{BD}{8} \implies BD=8 \sin72^{\circ} [/tex]

In triangle BCD,

∠CBD=34° (isosceles triangle)

∠DCB=116° (sum of angles in a triangle)

[tex]\frac{BC}{\sin 34^{\circ}}=\frac{8\sin 72^{\circ}}{\sin 116^{\circ}} \\ \\ BC=\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]

Answer:

4.59 cm to nearest hundredth.

Step-by-step explanation:

Consider triangle ABD.

sin 72 = DB / 8

DB = 8 sin 72

      = 7.608 cm.

Imagine a line from point C perpendicular to DB at point E.

As triangle CDB is isosceles ( DC = BC), this line will cut DB in 2

so, DE = 1/2 * 7.608 = 3.804.

Now consider triangle DCE which is a right-angled triangle at E.

cos 34 = 3.804 / DC

DC = 3.804 / cos 34

      = 4.588 cm

BC = DC = 4.588.

If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.

Pythagoras Theorem states that the sum square of two sides of triangle is equal to the  square of longest side.

Let us take Pythagorean triplet as (6,8,10).

where base=6

perpendicular = 8

hypotenuse = 10

Part(a)

Let us double the length of each value

base = 12

perpendicular = 16

hypotenuse = 20

By Pythagoras Theorem

[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}[/tex]

[tex]12^{2} +16^{2} =20^{2} \\ \\ 144+256=400\\ \\ 400=400[/tex]

Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.

Part (b)

Let us halve the length of each value

base=3

perpendicular = 4

hypotenuse = 5

By Pythagoras Theorem

[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}\\\\3^{2} +4^{2} =5^{2}[/tex]

[tex]9+16=25\\ \\ 25=25[/tex]

Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.

Therefore ,  If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.

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Answer:

let the complementary angle be x

51.1°+x=90°

x=90°-51.1°

x=38.9°

Answer: $3.40 per pint

Step-by-step explanation:

1 gallon=8 pints

3 gallons * 8 pints/1 gallon=

3*8/1=

3*8=24 pints in 3 gallons

$81.6 for 24 pints of paint

81.6/24=$3.40 per pint

Answer:

the value it's -21

Step-by-step explanation:

5×(-4)+3×(-5)+14=

-20 + (-15) + 14=

-20 -15 + 14=

-35 + 14=

-21.

Answer: Small box has the lowest amount when divided, that box has the best value.

Step-by-step explanation:

Given data,

Big box = 500 g

It cost is $8.00

Small box = 300 g

It cost is $ 5.40

First switch the box that's in kilograms into grams.

One kilogram=1000 grams.

Then,    Big box = 500 g = $ 8.00

            Small box = 300 g = $ 5.40

Next divide the amount in each box by the cost of each box.

           Big box = 500/8

           Big box  = 62.5

           Small box = 300/540

           Small box  = 0.5555

Therefore,

So, since small box has the lowest amount when divided, that box has the best value.

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